Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale p*. This scale appears to vanish faster than the Compton scale, mc, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behaviour observed on the lattice.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζτ(k) controlling the singularities for both the longitudinal  and transverse (τ = t) dynamical structure factors for the whole momentum range  , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data

Numerous sources of evidence point to the fact that heterogeneity within the Earth's deep crystalline crust is complex and hence may be best described through stochastic rather than deterministic approaches. As seismic reflection imaging arguably offers the best means of sampling deep crustal rocks in situ, much interest has been expressed in using such data to characterize the stochastic nature of crustal heterogeneity. Previous work on this problem has shown that the spatial statistics of seismic reflection data are indeed related to those of the underlying heterogeneous seismic velocity distribution. As of yet, however, the nature of this relationship has remained elusive due to the fact that most of the work was either strictly empirical or based on incorrect methodological approaches. Here, we introduce a conceptual model, based on the assumption of weak scattering, that allows us to quantitatively link the second-order statistics of a 2-D seismic velocity distribution with those of the corresponding processed and depth-migrated seismic reflection image. We then perform a sensitivity study in order to investigate what information regarding the stochastic model parameters describing crustal velocity heterogeneity might potentially be recovered from the statistics of a seismic reflection image using this model. Finally, we present a Monte Carlo inversion strategy to estimate these parameters and we show examples of its application at two different source frequencies and using two different sets of prior information. Our results indicate that the inverse problem is inherently non-unique and that many different combinations of the vertical and lateral correlation lengths describing the velocity heterogeneity can yield seismic images with the same 2-D autocorrelation structure. The ratio of all of these possible combinations of vertical and lateral correlation lengths, however, remains roughly constant which indicates that, without additional prior information, the aspect ratio is the only parameter describing the stochastic seismic velocity structure that can be reliably recovered.

A New Class of Nonionic Photosensitive Surfactants: Some Insights Concerning Conformations

We report on a new class of nonionic, photosensitive surfactants consisting of a polar di(ethylene oxide) head group attached to an alkyl spacer of between two and eight methylene groups, coupled through an ether linkage to an azobenzene moiety. Structural changes associated with the interconversion of the azobenzene group between its cis and trans forms as mediated by the wavelength of an irradiating light source cause changes in the surface tension and self-assembly properties. Differences in saturated surface tensions (surface tension at concentrations above the CMC) were as high as 14.4 mN/m under radiation of different wavelengths. The qualitative behavior of the surfactants changed as the spacer length changed, attributed to the different orientations adopted by the different surfactants depending on their isomerization states, as revealed by neutron reflection studies. The self-assembly of these photosensitive surfactants has been investigated by light scattering, small angle neutron scattering, and cryo-TEM under different illuminations. The significant change in the self-assembly in response to different illumination conditions was attributed to the sign change in Gaussian rigidity, which originated from the azobenzene photoisomerization.

Strukturbildung doppelthydrophiler Blockcopolymere mit mehrwertigen organischen Gegenionen

Sowohl die Komplexierung von Polyelektrolyten mit anorganischen Salzen, als auch die mit entgegengesetzt geladenen Polymeren wurde von vielen Autoren bereits intensiv untersucht. Doch gerade mit Molekülen die zwischen diesen beiden Extremen liegen, sollte es möglich sein, durch elektrostatische Wechselwirkungen gezielt nanometergroße Teilchen definierter Struktur herzustellen. Ziel dieser Arbeit war es deshalb, die Strukturbildung doppelthydrophiler Blockcopolymere mit mehrwertigen organischen Gegenionen zu untersuchen und insbesondere Parameter für die Bildung supramolekularer Strukturen in wässriger Lösung zu finden. Als Blockcopolymer wurde dabei Polyethylenoxid-b-methacrylsäure mittels anionischer Polymerisation hergestellt und mittels Gelpermeationschromatographie (GPC) und Kernresonanzspektroskopie (NMR)charakterisiert. Die Strukturbildung des Polyelektrolyten mit mehrwertigen organischen Gegenionen wurde in pH = 6- und pH = 7-Pufferlösung mit dynamischer und statischer Lichtstreuung, Kleinwinkelneutronenstreuung und Ultrazentrifugation untersucht. Mit Diaminobenzidin als Gegenion wurden dabei sphärische Komplexe mit einem hydrodynamischen Radius um 100 nm erhalten und mit Ultrazentrifugation der Anteil des Gegenions im Komplex quantifiziert. Die schlechte Löslichkeit des Diaminobenzidins in wässrigem Medium erschwerte allerdings die Interpretation der Ergebnisse. Trotzdem deuten diese darauf hin, dass keine Kolloidbildung des Diaminobenzidins, sondern eine Komplexierung der Einzelmoleküle mit dem Copolymer vorliegt. Um Probleme mit der Löslichkeit zu vermeiden, wurden schliesslich Polyamidoamin-Dendrimere als Gegenionen verwendet. Dabei wurde in pH = 6- und pH = 7-Pufferlösung für Dendrimere der Generation 4 mit steigender Gegenionenkonzentration ein kontinuierlicher Anstieg des hydrodynamischen Radius bis zu einer Größe von 70 nm gefunden. Mit Kleinwinkelneutronenstreuung konnte eine ellipsoidale Struktur dieser Komplexe beobachtet werden. Auch die Größe der Gegenionen spielt für die Bildung supramolekularer Aggregate eine Rolle. So zeigte sich, dass für Polyamidoamin-Dendrimere der Generation 2, analog zu denen der Generation 4, ein Anstieg des hydrodynamischen Radius mit steigender Gegenionenkonzentration zu beobachten ist. Für Generation 0-Dendrimere hingegen wurde ein umgekehrter Verlauf beobachtet, welcher dem für Diaminobenzidin gleicht. Somit kann man annehmen, dass die Aggregation mit kleinen Molekülen zu einer anderen Struktur der Komplexe führt, als die mit größeren Molekülen.

Crystalline, Mixed-Valence Manganese Analogue of Prussian Blue: Magnetic, Spectroscopic, X-ray and Neutron Diffraction Studies

The compound of stoichiometry Mn(II)3[Mn(III)(CN)6]2·zH2O (z = 12−16) (1) forms air-stable, transparent red crystals. Low-temperature single crystal optical spectroscopy and single crystal X-ray diffraction provide compelling evidence for N-bonded high-spin manganese(II), and C-bonded low-spin manganese(III) ions arranged in a disordered, face-centered cubic lattice analogous to that of Prussian Blue. X-ray and neutron diffraction show structured diffuse scattering indicative of partially correlated (rather than random) substitutions of [Mn(III)(CN)6] ions by (H2O)6 clusters. Magnetic susceptibility measurements and elastic neutron scattering experiments indicate a ferrimagnetic structure below the critical temperature Tc = 35.5 K.

Molecular-Based Magnetism in Bimetallic Two-Dimensional Oxalate-Bridged Networks. An X-ray and Neutron Diffraction Study

Bimetallic, oxalate-bridged compounds with bi- and trivalent transition metals comprise a class of layered materials which express a large variety in their molecular-based magnetic behavior. Because of this, the availability of the corresponding single-crystal structural data is essential to the successful interpretation of the experimental magnetic results. We report in this paper the crystal structure and magnetic properties of the ferromagnetic compound {[N(n-C3H7)4][MnIICrIII(C2O4)3]}n (1), the crystal structure of the antiferromagnetic compound {[N(n-C4H9)4][MnIIFeIII(C2O4)3]}n (2), and the results of a neutron diffraction study of a polycrystalline sample of the ferromagnetic compound {[P(C6D5)4][MnIICrIII(C2O4)3]}n (3). Crystal data:  1, rhombohedral, R3c, a = 9.363(3) Å, c = 49.207(27) Å, Z = 6; 2, hexagonal, P63, a = 9.482(2) Å, c = 17.827(8) Å, Z = 2. The structures consist of anionic, two-dimensional, honeycomb networks formed by the oxalate-bridged metal ions, interleaved by the templating cations. Single-crystal field dependent magnetization measurements as well as elastic neutron scattering experiments on the manganese(II)−chromium(III) samples show the existence of long-range ferromagnetic ordering behavior below Tc = 6 K. The magnetic structure corresponds to an alignment of the spins perpendicular to the network layers. In contrast, the manganese(II)−iron(III) compound expresses a two-dimensional antiferromagnetic ordering.

Neutron-mapping polymer flow: Scattering, flow visualization, and molecular theory

Flows of complex fluids need to be understood at both macroscopic and molecular scales, because it is the macroscopic response that controls the fluid behavior, but the molecular scale that ultimately gives rise to rheological and solid-state properties. Here the flow field of an entangled polymer melt through an extended contraction, typical of many polymer processes, is imaged optically and by small-angle neutron scattering. The dual-probe technique samples both the macroscopic stress field in the flow and the microscopic configuration of the polymer molecules at selected points. The results are compared with a recent tube model molecular theory of entangled melt flow that is able to calculate both the stress and the single-chain structure factor from first principles. The combined action of the three fundamental entangled processes of reptation, contour length fluctuation, and convective constraint release is essential to account quantitatively for the rich rheological behavior. The multiscale approach unearths a new feature: Orientation at the length scale of the entire chain decays considerably more slowly than at the smaller entanglement length.

The structure of the rare-earth phosphate glass(Sm2O3)0.205(P2O5)0.795 studied by anomalous dispersion neutron diffraction

The role of the Sm3+ ions in the structure of vitreous Sm2O3•4P2O5 has been investigated using the neutron diffraction anomalous dispersion technique, which employs the wavelength dependence of the real and imaginary parts of the neutron scattering length close to an absorption resonance. The data described here represent the first successful complete neutron anomalous dispersion study on an amorphous material. This experimental methodology permits one to determine exclusively the closest Sm• •• Sm separation. Knowledge of the R•••R (R = rare-earth) pairwise correlation is key to understanding the optical and magnetic properties of rare-earth phosphate glasses. The anomalous difference correlation function, ΔT''(r), shows a dominant feature pertaining to a Sm•••Sm separation, centred at 4.8 Å. The substantial width and marked asymmetry of this peak indicates that the minimum approach of Sm3+ ions could be as close as 4 Å. Information on other pairwise correlations is also revealed via analysis of T (r) and ΔT (r) correlation functions: Sm3+ ions display an average co-ordination number, n Sm(O), of 7, with a mean Sm–O bond length of 2.375(5) Å whilst the PO4 tetrahedra have a mean P–O bond length of 1.538(2) Å. Second- and third-neighbour correlations are also identified. These results corroborate previous findings. Such consistency lends support to the application of the anomalous dispersion technique to determine separations.

Determination of toluene hydrogenation kinetics with neutron diffraction

Total neutron scattering has been used to follow the hydrogenation of toluene-d₈ to methylcyclohexane-d₁₄ over 3 wt% platinum supported on highly ordered mesoporous silica (MCM-41) at 298 K and under 150 mbar D₂ pressure. The detailed kinetic information so revealed indicates that liquid reorganisation inside pores is the slowest step of the whole process. Additionally, the results were compared with the reaction performed under 250 mbar D₂ pressure as well as with toluene-h₈ hydrogenation using D₂ at 150 mbar.

Intermolecular vibrations and fast relaxations in supercooled ionic liquids

Short-time dynamics of ionic liquids has been investigated by low-frequency Raman spectroscopy (4 < omega < 100 cm(-1)) within the supercooled liquid range. Raman spectra are reported for ionic liquids with the same anion, bis(trifluoromethylsulfonyl)imide, and different cations: 1-butyl-3-methylimidazolium, 1-hexyl-3-methylimidazolium, 1-butyl-1-methylpiperidinium, trimethylbutylammonium, and tributylmethylammonium. It is shown that low-frequency Raman spectroscopy provides similar results as optical Kerr effect (OKE) spectroscopy, which has been used to study intermolecular vibrations in ionic liquids. The comparison of ionic liquids containing aromatic and non-aromatic cations identifies the characteristic feature in Raman spectra usually assigned to librational motion of the imidazolium ring. The strength of the fast relaxations (quasi-elastic scattering, QES) and the intermolecular vibrational contribution (boson peak) of ionic liquids with non-aromatic cations are significantly lower than imidazolium ionic liquids. A correlation length assigned to the boson peak vibrations was estimated from the frequency of the maximum of the boson peak and experimental data of sound velocity. The correlation length related to the boson peak (similar to 19 angstrom) does not change with the length of the alkyl chain in imidazolium cations, in contrast to the position of the first-sharp diffraction peak observed in neutron and X-ray scattering measurements of ionic liquids. The rate of change of the QES intensity in the supercooled liquid range is compared with data of excess entropy, free volume, and mean-squared displacement recently reported for ionic liquids. The temperature dependence of the QES intensity in ionic liquids illustrates relationships between short-time dynamics and long-time structural relaxation that have been proposed for glass-forming liquids. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3604533]

Structural, Magnetic and Thermal Studies of Ce1-xEuxCrO3 Nano-Powders

A new series of nano-sized Ce1-xEuxCrO3 (x = 0.0 to 1.0) with an average particle size of 50 - 80 nm were synthesized using a solution combustion method. Nano-powders Ce1-xEuxCrO3 with the canted antiferromagnetic property exhibited interesting magnetic behaviours including the reversal magnetization and the exchange bias effect. The effect of europium doping as the ion with the smaller radius size and different electron con figuration on structural, magnetic and thermal properties of Ce1-xEuxCrO3 were investigated using various experimental techniques, i.e. DC/AC magnetic susceptibility, heat capacity, thermal expansion, Raman scattering, X-ray photoemission spectroscopy, transmission/scanning electron microscopy, X-ray powder diffraction and neutron scattering. An exchange bias effect, magnetization irreversibility and AC susceptibility dispersion in these samples confirmed the existence of the spin disorder magnetic phase in Ce1-xEuxCrO3 compounds. The exchange bias phenomenon, which is assigned to the exchange coupling between glassy-like shell and canted antiferromagnetic core, showed the opposite sign in CeCrO3 and EuCrO3 at low temperatures, suggesting different exchange interactions at the interfaces in these compounds. The energy level excitation of samples were examined by an inelastic neutron scattering which was in good agreement with the heat capacity data. Neutron scattering analysis of EuCrO3 was challenging due to the large neutron absorption cross-section of europium. All diffraction patterns of Ce1-xEuxCrO3 showed the magnetic peak attributed to the antiferromagnetic Cr3+ spins while none of the diffraction patterns could detect the magnetic ordering of the rare-earth ions in these samples.

Self-assembly of an amyloid peptide fragment–PEG conjugate: lyotropic phase formation and influence of PEG crystallization

The self-assembly of PEGylated peptides containing a modified sequence from the amyloid beta peptide, YYKLVFF, has been studied in aqueous solution. Two PEG molar masses, PEG1k and PEG3k, were used in the conjugates. It is shown that both YYKLVFF–PEG hybrids form fibrils comprising a peptide core and a PEG corona. The fibrils are much longer for YYKLVFF–PEG1k, pointing to an influence of PEG chain length. The beta-sheet secondary structure of the peptide is retained in the conjugate. Lyotropic liquid crystal phases, specifically nematic and hexagonal columnar phases, are formed at sufficiently high concentration. Flow alignment of these mesophases was investigated by small-angle neutron scattering with in situ steady shearing in a Couette cell. On drying, PEG crystallization occurs leading to characteristic peaks in the X-ray diffraction pattern, and to lamellar structures imaged by atomic force microscopy. The X-ray diffraction pattern retains features of the cross-beta pattern from the beta-sheet structure, showing that this is not disrupted by PEG crystallization.